derivative of arcsin(a/x)

Lösung

\frac{d}{d x} (arcsin (\frac{a}{x}))

- \frac{a}{x x ^{2} - a ^{2}}

Schritte zur Lösung

\frac{d}{d x} (arcsin (\frac{a}{x}))

Wende die Kettenregel an:

\frac{1}{1 - ( \frac{a}{x} ) ^{2}} \frac{d}{d x} (\frac{a}{x})

= \frac{1}{1 - ( \frac{a}{x} ) ^{2}} \frac{d}{d x} (\frac{a}{x})

\frac{d}{d x} (\frac{a}{x}) = - \frac{a}{x ^{2}}

= \frac{1}{1 - ( \frac{a}{x} ) ^{2}} (- \frac{a}{x ^{2}})

Vereinfache

\frac{1}{1 - ( \frac{a}{x} ) ^{2}} (- \frac{a}{x ^{2}}) : - \frac{a}{x x ^{2} - a ^{2}}

= - \frac{a}{x x ^{2} - a ^{2}}

\int \frac{x ^{3} - 2 x ^{2} + 5 x - 2}{x ^{3} - 2 x ^{2} + x} d x

\frac{d}{d x} (- 2 sin^{2} (x))

n = 1 \sum \infty \frac{( ln ( 3 n ) )}{n}

d er i v a t i v e (2 x - 3)^{6}

e x p an d 3 x (2 + x)